Range of effectiveness of hydraulic diameter model as an analytical solution for rectangular microchannels

Abstract

Hypothesis: Spontaneous capillary flow in rectangular microfluidic channels is employed in microfluidic devices for various applications. The exact solution for flow in a rectangular cross-sectional channel has a complex point that contains an infinite sum term. The flow depends on the depth-width ratio of the rectangular channel's cross-section, ε. In previous studies, several approximations from exact solutions were useful for ε values smaller than 1 or 2. In this study, we propose a conversion equation J(ε) that turns the hydraulic-diameter (HD) model into a rectangular-channel (RC) model. Experiments: Rectangular type flow experiments with ethanol solution were conducted to confirm the difference between the RC and HD models when the analysis was performed based on each model. Findings: J(ε) depends on ε. At ε=0.441,2.27, the two models coincide. For 0.247<ε<4.04, J(ε) deviates by ±12.5%.

Keywords

• Microfluidic channel
• Capillary flow
• Rectangular channel
• Hydraulic diameter